Following [1]}, we begin by writing ansätze
for the fields of linearised
\({\cal N}=0\)  supergravity as the convolution product of two
copies of linearised Yang-Mills (one untilded and one tilded), as follows:
\(\varphi &=& A^\rho \circ {{\widetilde{A}}}_\rho + \alpha _1\,c^\alpha \circ {{\tilde{c}}}_\alpha +\alpha _2\, {\square ^{-1}}\, ({\partial }A\circ {\partial }{{\widetilde{A}}})\,,\\h_{\mu \nu } &=& A_{(\mu }\circ {{\widetilde{A}}}_{\nu )} + a_1\, {\square ^{-1}}\,{\partial }_\mu {\partial }_\nu \,(A^\rho \circ {{\widetilde{A}}}_\rho ) +a_2\, {\square ^{-1}}\, {\partial }_\mu {\partial }_\nu (c^\alpha \circ {{\tilde{c}}}_\alpha )\nonumber \\&& +a_3\, {\square ^{-1}}\, \Big ({\partial }A\circ {\partial }_{(\mu } {{\widetilde{A}}}_{\nu )} +{\partial }_{(\mu } A_{\nu )}\circ {\partial }{{\widetilde{A}}}\Big ) +a_4\, {\square ^{-2}}\,{\partial }_\mu {\partial }_\nu ({\partial }A\circ {\partial }{{\widetilde{A}}}) \nonumber \\&& +\eta _{\mu \nu }\,\Big (b_1\, A^\rho \circ {{\widetilde{A}}}_\rho +b_2\,c^\alpha \circ {{\tilde{c}}}_\alpha + b_3\, {\square ^{-1}}\, ({\partial }A\circ {\partial }{{\widetilde{A}}}) \Big )\,,\\B_{\mu \nu } &=& A_{[\mu } \circ {{\widetilde{A}}}_{\nu ]} +\gamma \,{\square ^{-1}}\, ({\partial }A\circ {\partial }_{[\mu } {{\widetilde{A}}}_{\nu ]}-{\partial }_{[\mu }A_{\nu ]}\circ {\partial }{{\widetilde{A}}})\,,\) 
